A continuous production process with continuous feeds and output products could be illustrated as FIG. 1. In FIG. 1, A is the upstream unit group of process, and the products of A are the raw material of the process unit B, while the products of B are the raw material of downstream processing unit group C. Because the number of the kinds of products of B may be more than one and these products may be feed to a plurality of downstream production units, these downstream production units are referred to as downstream unit group C. It must be pointed out that these material flows are continuous in cascade. In the unit B, there may be some key manipulating variables U, which are related to the technical objectives J such as the energy consumption, the economic benefits, the yields of the products and so on, the variables U can be referred to the input of the production unit(s), and J could be regarded as the output of the production process of B. The task of real time optimization is to maximize the objective (one or more targets combined, such as the economic benefit and the energy consumption) in a prescribed period of time by manipulating the key variables, as show in FIG. 2. It must be noticed that the objective may be switched according to the requirement of the production procedure.
To describe optimization with single objective function, the following equation can be generally used:J*=J(U*)=UmaxJ(U)  (1-1)
In the equation, J denotes the objective function, and J* denotes the optimum of the objective function J; while U is the operational variable, or is referred to as the optimized variable. U* is the optimum of the turning variable.
Generally, the functional relationship J (U) between U and J is an unknown analytically. For getting U*, two methods are commonly used: Mathematical Modeling and Online Search Methods.
1. Mathematical Modeling Method
The principle of the modeling method is to build a mathematical model of the objective function J and the optimized variable U firstly, and then to evaluate U* with nonlinear or linear programming based on the mathematical model and the constraints.
According to the different model building principles, mathematical modeling could be classified into mechanism modeling and experience modeling.
Mechanism modeling combines the operation mechanism equations of all parts of the equipment in the system according to the flow structures on the basis of the mass and energy balance principles, which forms a set of mathematical equations adaptable for the real production procedures. Finally, the relationship among the objective function and the optimized variable U is decided according to the systematical input and output, the price, and so on.
Whereas, if the described procedure is too complex, if the mechanism itself is not clear, or if the basic equation is not accuracy enough, it is often difficult to build the mechanism model. Moreover, the mechanism model of a system is generally not universal; it is even necessary to modify or change completely the model when the product and/or the feed are changed or when the process is slightly modified.
Experience modeling is to fabricate the experiential relationship between the optimized variable and the objective function based on plenty of data of the experiments and the daily operational report. The advantages of this kind of modeling are simple and universal. No matter how complex and different the procedure or the system is, the same simple method could be used to build the model, and no special process knowledge and pretest equations are needed.
However, the reliability of this method is not very good. If the operational range departs or oversteps the data sampling range when the model is built during online application, the error of model may be too much to be applied normally. Slight change of the process equipment may cause huge change of the model structure, which results in failure of the modelling works.
2. Online Search Method
Search method is a kind of universal method, the basic principle of the method is to change the value of the optimized variables on line, to observe the changing of the objective function, and then to decide whether the changing direction of the optimized variables is right. In principle, many nonlinear programming methods, such as the golden section method, could be used on line. However, this method is often very sensitive to the disturbance. It is well known that the objective function is not only the function of the optimized variables, but also the function of other uncontrollable variables (environmental variables). Thus, when the objective function is changed, it is difficult for the skilled in the art to judge whether it is caused by changes of the optimized variables or by the disturbance. In the present online search methods, the relationship between the optimized variables and the objective function is generally taken as the sole causation. Therefore, when there is the environmental disturbance, wrong judgment may be made, which could even cause reverse actions.
It is needed to point out, both of modeling and the direct search method are generally built on the basis of the mathematical descriptions of 1-1. The relationship between the objective function J and U is defined as the algebra map, without the environmental disturbance items. As a result, calculation methods educed therefore is only adaptable to the static and non-disturbance systems in principle.
In fact, situations are much more complicated. Firstly, there are not only the cause and effect relationship between the turning variables and the objective function logically, but also the dynamic procedures by time. That is, when the turning variables change, the objective function doesn't change immediately, but has a transition procedure. Secondly, from the view of real conditions of lots of industrial procedures, the objective functions often fluctuate. It is difficult to find a static condition. This is generally caused by those immeasurable and uncontrollable severe disturbances. For example, in the production procedure, the changes of component of feed often are uncontrollable. Due to the difficulties of online component measurement, these variables usually are immeasurable. On the other hand, a lot of procedures are sensitive to the changes of component. As a result, the influence of changes of component on the objective function is often larger, which could be several decade times some time, than that of the controllable factors, such as temperatures, pressures, and so on. Therefore, the fluctuation caused by the variation of the turning variables often is “submerged” in the disturbance of the component on the objective function. In this dynamic disturbance situation, any research task on realizing the turning operation has both practical and academic meanings.